[Nek5000-users] stokes flow with time-dependent boundary

Wed Dec 21 15:29:27 CST 2011

On 12/21/2011 10:17 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> Hi Lailai,
>
> I suggest initially starting with a single run, using steady Stokes.
> (Note, steady Stokes works only for Pn-Pn-2, so set lx2,ly2 = lx1-2, 
> etc.)
>
yes, this is what i did before, solving the Kovasznay problem in the 
tutorial using steady Stokes. The way i used is simply setting DENSITY 
to be zero in the .rea file, is this the right way to solve the steady 
Stokes problem? it seems work out for me, as the numerical results 
agreed very well with the analytical ones.

lailai
> Paul
>
>
> On Wed, 21 Dec 2011, nek5000-users at lists.mcs.anl.gov wrote:
>
>> thank you for your tip, Paul.
>>
>> i think we are solving a series of Stokes problems linked by a 
>> time-dependent boundary condition.
>> The time-derivative term is zero and we are not solving an unsteady 
>> Stokes problem.  I think we are not clear how to solve a series of 
>> Stokes problems.
>>
>> lailai
>>
>>
>>
>>
>>
>> On 12/21/2011 06:47 PM, nek5000-users at lists.mcs.anl.gov wrote:
>>> Hi Lailai,
>>>
>>> To switch to unsteady Stokes, you simply set the flag
>>> IFNAV to "F" in the .rea file, which turns off the convective
>>> term and simultaneously eliminates the CFL timestep constraint.
>>>
>>> [  Set:
>>>
>>>   T F F F F F F F F F F IFNAV & IFADVC (convection in P.S. fields)
>>>
>>> to
>>>
>>>   F F F F F F F F F F F IFNAV & IFADVC (convection in P.S. fields)
>>>
>>> .]
>>>
>>> It's still not clear to me if you are solving an unsteady
>>> Stokes problem, or a series of steady Stokes problems.
>>> (There is a difference...)
>>>
>>> Nek can handle either case with equal ease.
>>>
>>> I hope this helps.
>>>
>>> Paul
>>>
>>>
>>> On Wed, 21 Dec 2011, nek5000-users at lists.mcs.anl.gov wrote:
>>>
>>>> On 12/19/2011 06:17 PM, nek5000-users at lists.mcs.anl.gov wrote:
>>>>>
>>>>> Hi Lailai,
>>>>>
>>>>> I have used the approach you proposed for solving multiple
>>>>> steady stokes problems... you use an artificially large
>>>>> timestep.  That works.
>>>>>
>>>>
>>>> thank for your reply, if understand correctly, here you are talking 
>>>> about the second approach i proposed. For each time step, we solve 
>>>> a transient problem with very large internal timestep to quickly 
>>>> get to the steady-state solution.
>>>> since i am very new to nek5000, thus  i am not sure how to 
>>>> implement this method which seems not trivial.
>>>>
>>>> On the other hand, i started from the first example of the 
>>>> Kovasznay problem. I remove the time-derivative and convection term 
>>>> by setting the density in .rea file to zero, the numerical results 
>>>> agree very well with the analytical solution with zero Re number. I 
>>>> guess here the solver is just inverting a matrix which seems 
>>>> feasible for a 2D problem but might be too expensive or inefficient 
>>>> for a 3D problem.
>>>>
>>>>
>>>>> If you really have a time-dependent boundary condition, there
>>>>> is no reason you can't just use the unsteady Stokes solver
>>>>> with whatever timestep is required to accurately resolve your
>>>>> temporal bcs.   Note that, in this case, you would indeed have
>>>>> the inertial term rho du/dt present in the physics.
>>>>>
>>>>
>>>>
>>>>> Paul
>>>>>
>>>>>
>>>>> On Mon, 19 Dec 2011, nek5000-users at lists.mcs.anl.gov wrote:
>>>>>
>>>>>> Hello, guys,
>>>>>>
>>>>>> i am a new guy to Nek5000, i saw the manual of nek5000 that it 
>>>>>> can solve the steady stokes flow.
>>>>>> i guess when i solve such a flow, do i need to set it as a 
>>>>>> transient simulation with time-derivative term included to get  a 
>>>>>> steady-state solution? or, i can solve it by a direct solver 
>>>>>> method to get the solution immediately?
>>>>>>
>>>>>> since i want to add some time-dependent boundary condition for 
>>>>>> the steady stokes flow, so it will be pretty nice if i can solve 
>>>>>> it using the direct solver, for each time step, i solve one 
>>>>>> stokes flow; if nek5000 cannot solve it in such a way, i guess i 
>>>>>> have to use the first way; then for each time step i have to 
>>>>>> solve a transient problem to approach the steady state with some 
>>>>>> artificial time step used.
>>>>>>
>>>>>> i am not sure if i have stated my problem clearly. hopefully you 
>>>>>> guys have some experience on the feasibility of the two ways 
>>>>>> mentioned above. Thank you in advance.
>>>>>>
>>>>>> lailai
>>>>>>
>>>>>>
>>>>>>
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